3.1 Analysis and Construction of Mobile Intelligent Learning System

The mobile intelligent learning system is based on the mobile platform and development environment. With the help of artificial intelligence, data mining, and other scientific and technological means, it judges the characteristic information of different learners’ learning feedback, cognitive structure, and the degree of knowledge access. The system automatically matches the teaching strategies. At the same time, teachers can improve the teaching means and classroom timely according to the student’s learning situation to realize the innovation and optimization of the teaching mode. In traditional international English teaching, the teaching method only tests the student’s learning through one-way teaching of knowledge to students and through questions, such as examinations or classes. The teaching process is relatively solidified. Indeed, bringing mobile learning systems into the teaching environment allows learners to guide and track the dynamic monitoring of students’ learning and continuously adjust teaching programs to make targeted teaching recommendations. The learning system architecture diagram under mobile technology mainly takes students and teachers as the primary intervention objects. The human–computer interaction interface information between students and teachers can be transmitted through diagnosing and recording students’ learning information and reasoning and optimizing teachers’ teaching strategies. The learning system can then be improved by intelligent processing of information data. Fig. 1 shows the main architecture of the learning system under mobile technology.

Fig. 1. Main architecture of the learning system under mobile technology.

Fig. 2. Teaching relation diagram under mobile learning system.

Fig. 1 presents the learning system database containing six content levels: course management, learning resources, communication community, student information, examination evaluation, and system management. By transmitting these contents to the mobile terminal through the communication network, information integration can be realized at the levels of the student, teacher, and administrator subjects. Teachers can update the teaching data by checking the students’ learning status. At the same time, education managers can also master the classroom performance and teaching feedback of both teaching sides through mobile terminals. The connection of different teaching subjects and teaching modules can realize the real-time update of teaching tasks and teaching evaluation and promote the optimization and innovation of the English teaching mode. Fig. 2 shows the teaching relationship under the mobile learning system.

The mobile learning system can effectively connect the student module, the teaching module, the knowledge base, the teacher module, and the interaction module so students’ learning can be effectively fed back in time with the help of the interaction module. Teachers can also evaluate the students’ cognitive ability and test learning effect, and the pertinence of teaching has been greatly improved. As one of the international common languages, English has great practicality and practicality. The diversity of students’ sources and the continuous improvement of teaching standards make the internationalization trend of English teaching mode gradually obvious. Improving English teaching mode requires targeted teaching improvement according to the teaching characteristics. Mobile technology has significant advantages in English teaching recommendations and teaching quality evaluations. This can ensure teachers’ dynamic grasp of teaching situations and learning classrooms, continuously improve the deficiencies in teaching, and realize the innovation of teaching mode.

3.2 English Learning Prediction based on Optimized RBF Neural Network

The vigorous development of the Internet and computers makes people pay more attention to educational information. Learning analysis technology is developing rapidly. The learning prediction model is essential for evaluating the quality of teaching and promoting teaching reform. Most scholars have constructed learning prediction models according to different educational environments, but the limitations of model parameters limit their application scope. Therefore, the design and processing method of the RBF network prediction model based on association rule optimization is proposed based on the current situation and the basic framework of the prediction model. RBF is a neural network structure for interpolation in high-dimensional space. As a feedforward and back-propagation network, it comprises input, hidden, and output layers ^[18]. The hidden layer is the radial base layer. The basis function of the nodes in this layer adopts the distance function, in which the radial basis function is the activation function. The radial basis function network only responds to the input weight vector in the near range, so it has good local approximation ability. Fig. 3 shows the radial basis function network model.

Fig. 3. Radial basis function network model.

The empirical calculation formula for the number of hidden layer neurons in the radial basis function and the mathematical expression of the activation function is expressed in formula (1).

where$m$is the number of neurons in the hidden layer;$n,l$is the number of input and output nodes, respectively;$\beta $is a constant value in the range of (1–10), $\left|\left|dist\right|\right|$is the activation function, and$e$is a natural constant. The RBF neural network takes RBF as the hidden unit ``base'' to form a hidden layer space, changes its input vector, and transforms the linear non-separability of low dimensional data into separability in high dimensional space, i.e., the change between the input layer and hidden layer is nonlinear. The change from the hidden layer to the output layer is linear. The characteristic of the RBF neural network is that the weight of the hidden layer is constant 1, and the excitation function of the hidden layer is the Gaussian function. The relationship between the input and output layers of the RBF neural network is expressed as formula (2).

In Eq. (2), $cj$ is the center of the hidden layer node,${\sigma _{j}}^{2}$ is the variance, and $v_{jk}$is the output weight. When the network parameter is only the weight of the output layer, the variance at this time can be calculated using the empirical formula, and the output value can be converted without iteration, as expressed in formula (3).

where$d\max $in the variance formula is the maximum Euclidean distance between the central points, and$h$is the number of nodes in the hidden layer. In the output value weights, $T,Y$is the expected output and actual output of the sample, respectively; $\phi $is the hidden RBF function, and $V$ represents the weights of the hidden layer and the output layer. At the same time, to reduce the output value weight fluctuation caused by too many samples, the RBF neural network is studied using the gradient descent method, and the error of the objective function is defined. The calculation formula is expressed in formula (4).

where $c$ represents the number of neurons in the output layer, and$tk,zk$ represents the expected output and actual output of the$k$output neuron, respectively. The input values corresponding to the RBF network algorithm seldom have non-zero excitation values. The low variability makes the fitting performance and learning speed of the function faster. On the other hand, when selecting the algorithm, the neural data center is prone to data errors because of random selection (Meng H. et al. 2018) ^[19]. Based on the particularity and complexity of the English teaching mode, this paper introduces association rules to realize the association analysis of teaching influencing factors to provide an improvement basis for the teaching mode. Association rules are an important part of data mining technology and are valuable in learning and teaching evaluations. The association rules can be used to correlate the factors affecting the quality of English teaching and to predict the innovation of teaching mode with its association analysis degree. Fig. 4 presents the operation framework of the improved RBF neural network based on the association rules.

Fig. 4. Improved RBF neural network framework based on association rules.

In Fig. 4, In the improvement stage of English teaching mode, the most important thing is to preprocess the basic information of students’ learning behavior and learning situation and then introduce association rules to analyze the relevance and impact between the students’ learning profile and the teachers’ teaching activities. Therefore, improving the data support for the innovation of international teaching mode is essential for predicting a student’s behavior. The association rules are implicit expressions in the form of $X\rightarrow Y$, where$X,Y$ is an itemset containing one or more items, and $X\cap Y=\Phi $ and $X,Y$ are the antecedents and consequent of association rules. Eq. (5) is a part of the calculation formula in association rules.

In Eq. (5), $\mathit{\sup }port\left(A\Rightarrow B\right)$ is the degree of support, which represents the percentage of $A\Rightarrow B$ contained in the transaction set $D$ in the rule $A\cup B$. $Confidence\left(A\Rightarrow B\right)$ is the confidence that refers to the percentage of transactions in the transaction set $D$ that contains itemset $A$ and itemset $B$. $Lift\left(A\Rightarrow B\right)$ refers to the degree of improvement, which is defined as the ratio of rule confidence to support. The strong association rule is the process of satisfying both the minimum support and confidence thresholds. If the support of the itemset is greater than or equal to the given threshold, it is called a frequent itemset. The RBF neural network is improved using association rules, i.e., the support and confidence are taken based on the RBF algorithm to select the data center, and the probabilistic random selection method was adopted to improve the pertinence of data selection. The mathematical expression is expressed as formula (6).

where $P_{c}(X)$ is the probability that the input sample is selected as the data center, $\mathit{\sup }port(X)$ and$Confidence(X)$ are the support and confidence between the corresponding value of the input sample and the predicted result, respectively, and$P_{C}(X)'$is the probability after standardization. The improved RBF algorithm based on association rules has good applicability in teaching evaluation, information data screening, and prediction. This can help teachers dynamically master teaching data when designing teaching plans, improving teaching models, and promoting teaching reform.

4.1 Algorithm Performance Test of English Teaching Mode based on Mobile Technology

When using the optimized RBF algorithm to predict the students’ learning situation, first determine the number of neural layers of the neural network. The number of neurons in the model was set to two in the input layer: one in the hidden layer and one in the output layer. The data set is selected from the management database of the English major teaching in a university. Sixty and forty percent of the data set was used as test and application data, respectively. The performance of the improved RBF algorithm for the association rules adopted in the study was tested, and the improved RBF algorithm for clustering was used as a comparison algorithm to explore its fitting effect under different numbers of centers, and the resulting data was sorted out and drawn into a graph. Fig. 5 presents the results.

Fig. 5 shows the fitting curve of the two improved algorithms when the number of centers is 20. The deviation between the sample test and sample training of the algorithm in Fig. 5(a) was large. The input value 0 was taken as the dividing point, and the sample test value with a positive input value had a floating range of 1–2. The maximum error fluctuation was 10.20%, and the value showed a turning downward trend in the later period. In Fig. 5(b), the RBF algorithm improved by the association rules had a good fitting effect in sample testing and training. Although there is little fluctuation when the input value is negative, the similarity of the two-sample data is high in the later stage, and the error fluctuation range is less than 1%.

Fig. 6 shows the fitting curve of the two improved algorithms when the number of centers is 30. Fig. 6(a) shows that the fluctuation error between the data test value and the training value under the clustering RBF algorithm is large, and the test output value is usually smaller than the sample training value. On the other hand, the difference between the sample test value and the output value of the training value in Fig. 6(b) was small. The overall fluctuation nodes were less than the clustering-improved RBF algorithm, and the error of the overall output value is no more than 3%. At the same time, compared to the results in Fig. 5, the fitting effect was also different because of the different number of initial centers selected. In addition, the approximation effect of the fitting curve of the clustering improved RBF algorithm was quite different, which was more likely to be affected by the number of centers and produce deviation.

In contrast, the improved RBF algorithm proposed in the study has good generalization ability and can realize the classification and prediction of data. At the same time, the error and convergence of the improved RBF algorithm adopted in the experimental process were collected, as shown in Fig. 7.

The approximation error and generalization error of the algorithm used in the study showed a downward trend with the increase in training time (Fig. 7). The error values of the two curves tend to be flat after 500 seconds. The approximation error values are smaller than the generalization error as a whole. The minimum error values of the two were 0.075 and 0.14, no more than 0.15. Moreover, the convergence performance of the improved RBF algorithm was improved greatly compared to that before the improvement. The slope of the improved convergence curve was lower than that before the improvement. The convergence of the algorithm was good when the training time was 2000 seconds, which shows that the algorithm has good applicability in processing data samples. The approximation effect of the sample test can better reflect the relationship and proximity between the test value and the real value of the algorithm. The approximation effect of the proposed algorithm was tested and compared with the traditional RBF algorithm, as shown in Fig. 8.

The results in Fig. 8 show that the values of the improved RBF algorithm are consistent with the actual output values, which are distributed on both sides of the output value curve. In contrast, the unmodified output values have a certain deviation from the curve, and some samples even have a long-distance deviation from the curve. The RBF algorithm is generally improved, and its approximation effect is better.

Fig. 5. Comparison results of fitting curves of two algorithms when the number of centers is 20.

Fig. 6. Comparison results of fitting curves of the two algorithms when the number of centers is 30.

Fig. 7. Performance results of data test based on Improved RBF algorithm with association rule.

Fig. 8. Approximation test results under different algorithms.

4.2 Analysis of English Teaching Application Test based on Improved RBF Algorithm

The learning platform supported by mobile technology classifies and processes various types of data and realizes their effective connection. The key to promoting the transformation of teaching mode lies in mastering and managing dynamic learning information. Therefore, the effect of information classification significantly correlates with the formulation of the goal of internationalization of English teaching. First, three data sets are selected from the experimental sample data for the application test, and the learning rate of the weight is set to 0.03. The algorithm used in the study is compared with the structure adaptive monitoring algorithm. The results are shown in Fig. 8. The adaptive supervision algorithm can effectively reduce the data dimensions and achieve the classification performance of data when processing nodes. Therefore, it is used as a comparison algorithm for application testing. Fig. 9 presents the experimental results.

Fig. 9(a) shows the classification accuracy of English information data under the three algorithms. The results show that the classification accuracy of the algorithm used in the study is the highest of the four data sets, which are 91.23%, 91.14%, 84.36%, and 81.28%, respectively, significantly higher than that of the supervised algorithm and the traditional RBF algorithm. When the test time on the data set was measured, the results in Fig. 9(b) show that the time consumption of the algorithm used in the study is only the same as that of the monitoring algorithm on data set 1. On the other hand, with the increased number of samples in the data set, the improved RBF algorithm can process the data better, with a higher classification efficiency and less than 30 seconds. It then analyzes the factors that influence the effect of English teaching and the internationalization of teaching mode. It explores the correlation between them with the help of the association rule algorithm, as listed in Table 1.

In Table 1, there was a high correlation between the teachers’ teaching philosophy, teaching process, teaching scheme formulation, classroom design and management, teaching pertinence, professional training of teaching ability, English communicative ability, international classroom teaching atmosphere under the teaching mode, and the correlation is basically above 0.15, of which the correlation coefficient between international teaching atmosphere and classroom design reaches 0.29. The characteristic factors that affect the international teaching mode of English are screened and sorted by importance, and five influencing factors with higher importance are selected, as shown in Fig. 9.

In Fig. 10, 1–5 characteristic factors are the classroom teaching atmosphere, teachers’ teaching level, teaching plan, feedback of students’ learning information, and emphasis on English communicative competence. The above five characteristic factors were of high importance and had obvious aggregation (Fig. 9). The importance of English communicative competence is approximately four points, which is an essential factor affecting the internationalization of teaching. The dissatisfaction evaluation scores of teachers and students before and after the application of the mobile English teaching platform were analyzed statistically to collect teaching information and provide a reference for promoting the international teaching mode of English. The results are presented in Fig. 11.

The dissatisfaction scores of teachers and students with the English teaching effect were 46.35 and 65.02 before applying the English teaching platform (Fig. 10). After the application, however, the dissatisfaction scores were 13.27 and 18.22, showing a 55.48% and 56.22% decrease, respectively. The data showed significant statistical significance (P < 0.05).

Fig. 9. Statistical results of the classification accuracy and time consumption under different algorithms.

Fig. 10. Screening results of characteristic factors influencing English internationalization teaching model.

Fig. 11. Statistics of dissatisfaction assessment scores of teachers and students before and after the application of the Mobile English teaching platform.